Rotor blade for a rotary machine

ABSTRACT

A rotor blade having a wing and beam construction for a tip shroud is disclosed. Various construction details are developed for providing the shroud with depression in the shroud and a transition zone that extends from the suction side and pressure side of the airfoil to provide a flow path surface of the shroud. In one detailed embodiment, the tip shroud has a depression generally outwardly of the airfoil and generally following the curve of the pressure and suction sides of the airfoil from the leading edge region to the trailing edge region.

TECHNICAL FIELD

This invention relates to rotor blades of the type used in industrialgas turbine engines, and more specifically, trout for the tip region ofsuch a rotor blade.

BACKGROUND OF THE INVENTION

Gas turbine engines for aircraft have rotor blades that typically aresmaller than rotor blades used in, for example, the turbine of anindustrial gas turbine that employs steam as a working medium

The rotor assembly employs such blades with a rotating structure, suchas a rotor disk, having an axis of rotation and a plurality of outwardlyextending blades. Each blade is disposed about a spanwise axis thatextends radially. Generally, the spanwise axis is a radial line referredto as the stacking line which extends outwardly on a radius from theaxis of the rotor blade. The rotor blade has a base, commonly called aroot, which engages the rotating structure at the inner end of theblade.

The rotor blades each have an airfoil which extends outwardly from theroot across the working medium flowpath. The rotor blade typically has ashroud extending between airfoils of adjacent rotor blades at the tipregion of the rotor blade. The shroud has cantilevered wings whichextend laterally (circumferentially) between adjacent rotor blades. Thewings include a portion of a transition zone that extends from thejunction with the airfoil that has an inwardly facing surface whichbounds the working medium flowpath. The shroud also has a seal landwhich extends circumferentially a close to adjacent stator structure toblock the working medium gases from leaving the flowpath. In someconstructions, a more rigid member extends between the front and rearportions of the wings to carry the seal land and provide a portion ofthe transitions zone.

The shrouds of adjacent rotor blades abut at contact areas on thelaterally sides of the shroud. The shrouds reduce blade deflectionsabout the spanwise axis and minimize vibration of the rotor blades.Damping of the blades takes place through rubbing of the contact facesof adjacent shrouds. Additional rotational loads are created by the massof the shroud as compared with rotor blades having no shrouds. Theserotational loads increase stresses at the shroud airfoil interfacebecause of the sudden change in cross-section of the material and at theroot-disk interface of the rotor blade and the desk. The stresses in theairfoil and the shroud of the rotor blades require heavier designs thannon-shrouded blades of equivalent cyclic fatigue life. In addition, themass of the shroud may cause creep of the airfoil and creep of portionsof the shroud in a radial direction because of rotational forcesgenerated under operative conditions.

Accordingly, scientists and engineers working on the direction ofapplicants assignee have sought to develop and to shrouds for rotorblades that reduce the concentrated stressors in the rotor blades anddemonstrate acceptable resistance to creep without causing additionalcreep in the airfoil by increasing the mass of the rotor blade.

SUMMARY OF THE INVENTION

A tip shroud for a rotor blade shroud attached to an airfoil by atransition zone includes wings extending from the sides of the airfoiland a beam which extends past the airfoil for carrying a seal land andbetween the wings to divide each wing into a front portion and a rearportion,

The surface contour of a transition zone for a rotor blade shroud at aparticular location is defined by the line of intersection of areference plane P with the surface of the transition zone. The referenceplane is referred to as the normal sectioning plane. The reference planepasses through the point at the junction of the transition zone and theairfoil. The junction point is usually the point of tangency of thetransition zone with the airfoil. The reference plane P contains a firstline perpendicular to the airfoil surface (airfoil section surface) atthe junction point and a second line parallel to the stacking line ofthe airfoil.

Accordingly, the normal sectioning plane P passes through the junctionpoint and is defined by two straight lines passing through the junctionpoint. As shown, for example, this provides an “X axis” which is a firststraight line in the plane of the airfoil section normal (perpendicular)to the surface of the airfoil section; and, a “Y-axis,” which isperpendicular to the first straight line and also parallel to thestacking line of the airfoil.

The line of intersection of the normal sectioning plane with thetransition zone is referred to as a transition line. As will berealized, lines of intersection between a plane and a surface may bestraight or curved depending on the orientation of the plane to thesurface. Accordingly, the term “transition line” includes straight linesand curved lines. In this application, the line of intersection isviewed perpendicular to the sectioning plane. The definition of the“offset ratio” for a transition line is the ratio of the length ordistance “A” of the projection of the transition line along the X-axisof the sectioning plane divided by the length or distnce “B” of theprojection of the transition line along the spanwise Y-axis. The lengthA is also referred to as the offset distance of the transition line (ortransition zone) from the airfoil and the length B is referred to as theoffset distance of the transition line from the shroud.

Bending or the bend of the transition line is a measure of the change inslope per unit length of the transition line as the transition lineextends away from the airfoil surface. Thus, at any location, thetransition line (transition zone) has a first end at the junction pointwith the airfoil and a second end at the location on the shroud wherethe remainder of the shroud extends in cantilevered fashion from thetransition zone. This location is where the associated transition linesmoothly joins the remainder of the shroud and the instantaneous changein slope is zero, such as at a point of tangency, or where the extensionof the transition line on the shroud reverses curvature and bendsoutwardly.

According to the present invention, a rotor blade includes a tip shroudhaving a depression generally outwardly of the airfoil and generallyfollowing the curve of the pressure and suction sides of the airfoilfrom the leading edge region to the trailing edge region, the tip shroudhaving wings extending from the sides of the airfoils, each wing havinga front portion and a rear portion which continue the surface of thedepression, the shroud further including a seal land extending past thesides of the airfoil between the front and rear portions of the wings.

In one embodiment, a beam which carries the seal land extends laterallyacross the depression to divide the depression into a front portion anda rear portion, and extends past the sides of the airfoil and isintegral with the wings to support the front and rear portions of thewings.

In one embodiment, the radial thickness of the wings is decreased by thedepression in the wings which decreases airfoil creep as compared to awing which does not have a radial depression.

In another embodiment, at least a portion of the wing includes atransition zone that extends from the side of the airfoil to provide aflow path surface of the shroud, the transition zone having across-sectional shape which is tapered to the side of the wing.

In one detailed embodiment, the transition line of the wing, which isalso the contour of the flow path surface of the shroud for thetransition zone of the wing, generally follows the shape of a conicalsection as it extends away from the airfoil and the depression above thetransition zone has a spanwise depth at a first lateral location that issmaller than the spanwise depth of the depression in the wing at asecond lateral location that is laterally closer to the airfoil.

In one detailed embodiment, the spanwise depth of the transition zone atthe first location is greater than the spanwise depth at the secondlocation.

In accordance with the present invention, the transition lines extendingunder the beam have a first radius of curvature adjacent the airfoil anda second radius of curvature adjacent the shroud that is larger than thefirst radius of curvature.

In accordance with one detailed embodiment of the present invention, thefirst and second radii of curvature intersect at a point of tangency.

In accordance with another detailed embodiment of the present invention,the intersection includes a straight line that is tangent to the firstand second radii of curvature.

In accordance with another detailed embodiment of the present invention,the intersection includes a curved line that is tangent to the first andsecond radii of curvature.

A primary advantage of the present invention is the efficiency of theengine and creep resistance of the airfoil and creep and bendingresistance of the shroud which results from reducing the shroud masswhile maintaining the overall configuration of the surface bounding theworking medium flow path by forming a depression which is generallyradially outwardly of the airfoil and tapering the wings of the shroud.

Another advantage of the present invention is the fatigue life of theshroud resulting from the level of the bending stresses in the wingswhich occurs from transferring a portion of the rotational loads on thewings through the beam to the transition zone under the beam to permitreducing the size of the transition zone under the wings.

In one particular embodiment, an advantage is the level of creepresistance of the shroud as compared to a solid shroud which is enhancedby providing a portion of the material removed to form the depressionsin the shroud and in the wings and providing a transition zone havingincreased mass at a location which is spanwise inwardly of the locationswhere shroud material was removed as compared to a shroud of the sameflowpath configuration which does not have a depression. This reducesrotational forces acting on the airfoil and increases creep resistanceof the airfoil and shroud under operative conditions.

The foregoing features and advantages of the present invention willbecome more apparent in light of the following detailed description ofthe invention and the accompanying drawings.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a front view of a rotor assembly

FIG. 2 is a side elevation view of the pressure side of a rotor blade;

FIG. 3 is a top view of two adjacent tip shrouds of the rotor assemblyshown in FIG. 1. side elevation view of the rotor blade shown in FIG. 2which is broken away to show the interior of the rotor blade;

FIG. 4 is a top view of the tip shroud shown in FIG. 3. taken along thelines 4-4 of FIG. 3 at about the forty (40) percent span of the airfoilshowing a front serpentine passage, a rear serpentine passage and athird leading edge passage and showing the minimum height of the passageas measured in a chordwise extending plane;

FIG. 5 is a side elevation view of the pressure side of the rotor bladein the tip region;

FIG. 6 is a side elevation view of the suction side of the rotor bladein the tip region;

FIG. 7 is a top view of the shroud showing the location of a normalsectioning plane at thirteen locations on the tip shroud and showing theextent of the transition zone extending on the shroud and as reported inTable 1 (FIG. 7 a);

FIG. 8, FIG. 9 and FIG. 10 are front, oblique, schematic perspectiveviews of the tip shroud shown in FIG. 2.

FIG. 11 is a rear, oblique, schematic perspective views of the tipshroud shown in FIG. 2.

FIGS. 12 and 13 are simple views of a conical section curve and a tworadius curve approximating the conical section curve.

DETAILED DESCRIPTION OF THE INVENTION

FIG. 1 is a simplified front elevation view of a rotor assembly 10 of arotary machine having an axis Ar. The rotor assembly includes a rotatingstructure, as represented by the disk 12, and a plurality of outwardlyextending rotor blades 14. Each rotor blade has a root 16 and an airfoil18 being disposed about a spanwisely extending axis S, which is commonlycalled the stacking line S. The airfoil has a pressure side 24 and asuction side 26. A flowpath 22 for working medium gases extends throughthe rotor blades between the sides of the airfoil.

The rotor blade has a tip region 28 having a tip shroud 30. The tipshroud includes a seal land 32 which is a surface having a radius ofcurvature about the axis Ar. The tip shroud has a transition zone 34which extends from the sides 24, 26 of the airfoil, as represented bythe pressure side. The transition zone includes part of a flowpathsurface which extends from a tangent to the pressure side of the airfoilalong a junction J.

FIG. 2 is a side elevation view of the rotor blade shown in FIG. 1. Theairfoil 18 has a leading edge 36 and a trailing edge 38. The tip shroudhas a laterally (circumferentially) extending beam 42 which carries theseal land.

FIG. 3 is a top view of a pair of adjacent tip shrouds 30. Each tipshroud has a leading edge region and a trailing edge region. The tipshroud includes a depression in the shroud generally radially outwardlyof the airfoil and generally following the curve in the tip region ofthe pressure and suction sides of the airfoil from the leading edgeregion to the trailing edge region.

The tip shroud includes a pressure side wing 52 extending from thepressure side of the airfoil having a front portion 52 f and a rearportion. The portions of the wing continue the surface of thedepression. The pressure side wing has a laterally facing pressure side.The tip shroud includes a suction side wing extending from the suctionside of the airfoil having a front portion and a rear portion. Theportions of the wing continue the surface of the depression. The suctionside wing has a laterally facing suction side.

The tip shroud further has the beam 42 which has a front face 42 f and arear face 42 r integral with the wings. The beam extends laterallybetween the wings to divide each wing into the front portion and therear portion and laterally across the depression to divide thedepression into a front portion 48 f and a rear portion 48 r. The beamfurther has a pressure side region 62 extending laterally past thepressure side of the airfoil in the tip region of the airfoil, and has alaterally facing pressure side 63 which adapts the beam to engage thesuction side 65 of the beam of the adjacent airfoil. The beam also has asimilar region on the suction side. The suction side region 64 extendslaterally past the suction side of the airfoil in the tip region of theairfoil, and has a laterally facing suction side which adapts thesuction side of the beam to engage the pressure side of the beam of theadjacent airfoil.

FIG. 4 is a top view of the rotor blade shown in FIG. 3. FIG. 5 and FIG.6 are side elevation views, respectively, of the pressure side andsuction side of the rotor blade. As mentioned, the seal land extendsradially outwardly from the beam. The seal land reinforces the beam. Thecombination of the seal land and beam extends to support the front andrear portions of the wings providing a portion of the support requiredagainst rotational forces acting on the wings under operativeconditions. Toward this end, the beam and seal land have an invertedT-shaped cross-sectional shape. The axial width Wb of the beam isgreater than four times the axial width Ws of the seal land and theradial height Hs of the seal land is greater than twice the height ofthe beam Hb. A fillet radius extends from the front face of the sealland to the front face of the beam and a fillet radius extends from therear face of the seal land to the rear face of the beam.

FIG. 5 and FIG. 6 also show the junction J of the transition zone withthe pressure side and suction side of the airfoil. The junction isformed by an infinite number of junction points each at the point oftangency of the transition zone to the airfoil. The tangency of the lineprovides a smooth transition. As will be realized, other types of smoothtransitions may exist although a tangent is preferred because of thesmooth change that occurs. A normal sectioning plane P is shown. Thenormal sectioning plane has a first line La perpendicular to the side ofthe airfoil at the point of tangency (junction point) and a second lineLsl passing through the junction point and parallel to the stacking lineS as discussed earlier. The offset distances A and B are shown. As canbe seen, the transition zone extends much further down on the pressureside of the airfoil than on the suction side of the airfoil.

FIG. 7 is a view from above of one representative airfoil section. Thesurface of the airfoil is defined by a plurality of these airfoilsections each extending perpendicular to the stacking line S. FIG. 7shows the relationship of the leading edge and the trailing edge to achord line having a length C which connects the leading edge in thetrailing edge. A mean chord line extends from the leading edge to thetrailing edge about midway between the suction side and the pressureside. The leading edge region extends about three percent of the lengthof the chord line along a line tangent to the mean chord line at theleading edge. A trailing edge region extending about three percent ofthe length of the chord line along a line tangent to the mean chord lineat the trailing edge,

FIG. 7 also shows thirteen normal sectioning planes intersecting thetransition zone, each having a line of intersection with the surface ofthe transition zone. The length of the offset distances A is shown. Eachsectioning plane shows that the transition zone extends to the side ofthe wings and under the beam to the extent shown by the curved linesnear plane 1 (B1) and plane 8 (B8).

Table 1 is a listing of the offset distances A, B and the offset ratioR=A/B. The offset ratio is also shown rounded to the nearest hundredths.As can be seen from inspection of the Table, the offset ratio is fairlylarge and the front portion of the suction side wing and under the beamon the suction side. The ratios are also greater than one underneath thebeam on the pressure side, but are smaller. This is attributable in partto the contouring of the transition zone which has more materialextending radially down the side of the airfoil on the pressure sidethan on the suction side as shown in FIG. 5 and FIG. 6.

The relationship of the offset ratios of the transition line a shown inthe following Figures. FIG. 8 is a simplified perspective view showing acircular transition line on the pressure side of the airfoil. The normalsectioning plane P passes through the junction point Js. The view is nottaken parallel to the normal sectioning plane. FIG. 9 is a similar viewof an elliptical transition line on the front wing of the pressure side.FIG. 10 is another front view similar to FIG. 9. FIG. 11 is a rear viewsimilar to FIG. 9 but showing the elliptical transition line extendingunder the beam.

As can be seen, the transition zone extending under the beam extends toa location between the pressure side of the airfoil and the pressureside of the beam. The transition zone ends at a location on the inwardlyfacing surface of the suction side region of the beam and between thesuction side of the airfoil and the suction side of the beam. Similarly,as shown in FIG. 7, the transition zone extends in the same manner onthe pressure side of the beam.

As can be seen from these figures, the transition zone oversubstantially all of its extent between the leading edge region and thetrailing edge region extends to the sides of the wings such that eachwing has a cross-sectional shape at a location along a normal sectioningplane that is spanwisely tapered to the sides of the wings, and that isspanwisely tapered under the beam at least as far as the immediatelyadjacent portion of the wing. In one particular embodiment, thetransition lines in the transition zone that extended only under thewings covered over ninety-nine (99) percent of the surface area of thetransition zone. In other embodiments, good results are expected wherethe transition lines extend to over ninety-five (95) percent of thetransition zone. As can be seen from the table, the cross-sectionalshape of the transition zone has more than one type of curvature toreduce stresses in the rotor blade as compared to transition zoneshaving one type of curvature for the transition zone. For example,offset ratios equal to one provide circular transition lines which onthe pressure side of the airfoil decreases surface stresses in theairfoil at the rare portion of the pressure side wing. Offset ratiosgreater than one provide elliptical shaped or true elliptical transitionlines reduce stress concentration factors better than circularcross-sections. They are heavier constructions than analogous circulartransition lines because more material is placed closer to the shroud atgreater radial distance from the axis Ar.

Conical section lines that represent the intersection of a plane with aright circular cone form transition lines that have the advantageousbenefits of reducing stress concentration factors. These curves may beused to form transition lines. Elliptical transition lines are oneexample. Another example are transition lines formed with curves ofmultiple radii that follow a conical section lines such as an ellipticaltransition line and may be formed. These curves are used on at least oneof said sides of the airfoil and show transition lines that extend underthe beam that have greater bending away from the airfoil at a regioncloser to the airfoil on the transition line than at a region closer tothe side of the shroud. As a result, and as shown in FIG. 7 and Table 1,the average of offset ratios Rb of transition lines that extend underthe beam are greater than one and are greater than the average of offsetratios Rw of transition lines that extend only under the rear portion ofwings. In fact, and embodiment shown, the absolute value of thetransition lines Rb is greater than the ratios Rw.

Thus, the transition lines which define the contour of the flow pathsurface of the shroud for the transition zone of the wing and of thebeam follow the shape of part of a conical section. They also have anoffset ratio on the suction side of the airfoil for the beam Rb and forthe forward portion of the wing Rw that is greater on average than theoffset ratio on the pressure side of the airfoil for the beam Rb and forthe rear portion of the wing Rw, thus providing a more ellipticalflowpath surface on the suction side beam-wing forward region to reducestress concentration factors in that region. They also provide a morecircular flowpath surface on the pressure side for the beam-rear wingportion to provide transition zone material that extends down theairfoil, the offset distance B, for at least 80% of the length that thematerial extends laterally on the shroud, offset distance A, to reduceairfoil surface stresses as compared to an airfoil not having such alength of shroud material.

These are more easily manufactured because curves with constant radiusor regions of constant radius are much easier to inspect. Thus, it isadvantageous to transfer some loads from a region and to use circularcurves (rear portions of wing) in those regions because the stressconcentration factor is less of a concern. In regions where the stressconcentration factor is of more concern curves of multiple radii may beused used to generate transition lines having a conical or almostconical curves. The advantage results because during manufacture, thetransition line curves must be inspected and have a profile tolerance.In applying the tolerances, the minimum radial dimension should not beviolated. However, when normal tolerances are applied in some locationson conical sections, it is difficult to determine if the curve hasviolated the minimum radius tolerance dimension. This is less severe andmay be eliminated if curved compound transition line is used. In thosecases, the inspection criteria set out can control the radii sizes byapplying a limit dimension to each of the radii.

FIGS. 12 and 13 are examples of a conical transition line and a tworadius curve fitted to a conical transition line. As will be realized,more than two curves could be used to generate the same transition line.

Although the invention has been shown and described with respect todetailed embodiments thereof, it shoud be understood by those skilled inthe art that various changes in form and detail may be made withoutdeparting from the spirit and scope of the claimed invention.

1. A rotor blade for rotary machine having a flowpath for working mediumgases, the rotor blade having an inner end which includes a base whichadapts the rotor blade to be joined to a rotatable structure, an outerend having a laterally extending surface which is disposedcircumferentially about an axis Ar and having a radius of curvatureabout the axis Ar, an airfoil having a leading edge, a trailing edge,and a suction side and a pressure side which each extend chordwise fromthe leading edge to the trailing edge, and a tip region which includesthe outer end, which comprises: a plurality of airfoil sections disposedspanwise about and perpendicular to the stacking line for defining thesurfaces of the airfoil, the stacking line of the airfoil extendingspanwise, and each airfoil section having a leading edge, a trailingedge spaced chordwise from the leading edge, a suction side extendingfrom the leading edge to the trailing edge, and a pressure sideextending from the leading edge to the trailing edge; a chord linehaving a length C, a mean chord line extending from the leading edge tothe trailing edge about midway between the suction side and the pressureside a leading edge region extending about three percent of the lengthof the chord line along a line tangent to the mean chord line at thetrailing edge, a trailing edge region extending about three percent ofthe length of the chord line along a line tangent to the mean chord lineat the trailing edge; a tip shroud for the rotor blade disposed in thetip region, the tip shroud including a depression in the shroudgenerally radially and outwardly of the airfoil and generally followingthe curve in the tip region of the pressure and suction sides of theairfoil from the leading edge region to the trailing edge region, wingsextending from the sides of the airfoil, the wings including a pressureside wing extending from the pressure side of the airfoil having a frontportion and a rear portion which continue the surface of the depression,and having a laterally facing pressure side a suction side wing thatextends from the suction side of the airfoil having a front portion anda rear portion which continue the surface of the depression, and havinga laterally facing suction side, and, a seal land extending radiallyoutwardly, the seal land extending past the sides of the airfoil betweenthe front and rear portions of the wings and having said outwardlyfacing surface which extends circumferentially with respect the axis Arand which adapts the seal land to cooperate with adjacent structure ofthe rotary machine to block the leakage of working medium gases past thetip region of the rotor blade.
 2. The invention as claimed in claim 1wherein the tip shroud further has a transition zone extending from ajunction with the suction side and a junction with the pressure side ofthe airfoil to provide a flow path surface of the shroud which has asmooth contour, and, wherein the pressure side wing has a portion of thetransition zone which extends from the pressure side of the airfoil,and, the suction side wing has a portion of a transition zone whichextends from the suction side of the airfoil.
 3. The invention asclaimed in claim 2 wherein the tip shroud further has a beam which has afront face and a rear face integral with the wings, which extendslaterally between the wings to divide each wing into a front portion anda rear portion and laterally across the depression to divide thedepression into a front portion and a rear portion, the beam furtherhaving a pressure side region extending laterally past the pressure sideof the airfoil in the tip region of the airfoil, having a laterallyfacing pressure side which adapts the beam to engage the suction side ofthe beam of the adjacent airfoil, a portion of the transition zone whichextends from the pressure side of the airfoil, a suction side regionextending laterally past the suction side of the airfoil in the tipregion of the airfoil, having a laterally facing suction side whichadapts the suction side of the beam to engage the pressure side of thebeam of the adjacent airfoil, a portion of the transition zone whichextends from the suction side of the airfoil, and wherein a seal landextending radially outwardly from the beam and wherein the beamreinforced by the seal land extends to support the front and rearportions of the wings to provide a portion of the support requiredagainst rotational forces acting on the wings under operativeconditions.
 4. The invention as claimed in claim 1 wherein the tipshroud further has a beam which has a front face and a rear faceintegral with the wings, which extends laterally between the wings todivide each wing into a front portion and a rear portion and laterallyacross the depression to divide the depression into a front portion anda rear portion, the beam further having a pressure side region extendinglaterally past the pressure side of the airfoil in the tip region of theairfoil, having a laterally facing pressure side which adapts the beamto engage the suction side of the beam of the adjacent airfoil, asuction side region extending laterally past the suction side of theairfoil in the tip region of the airfoil, having a laterally facingsuction side which adapts the suction side of the beam to engage thepressure side of the beam of the adjacent airfoil; and, wherein a sealland extends radially outwardly from the beam and wherein the beamreinforced by the seal land extends to support the front and rearportions of the wings to provide a portion of the support requiredagainst rotational forces acting on the wings under operativeconditions.
 5. The invention as claimed in claim 3 wherein the beam andseal land have an inverted T-shaped cross-sectional shape with the axialwidth of the beam being greater than four times the axial width of theseal land and the radial height of the seal land is greater than twicethe height of the beam with a fillet radius extending from the frontface of the seal land to the front face of the beam and a fillet radiusextending from the rear face of the seal land to the rear face of thebeam.
 6. The invention as claimed in claim 4 wherein the beam and sealland have an inverted T-shaped cross-sectional shape with the axialwidth of the beam being greater than four times the axial width of theseal land and the radial height of the seal land is greater than twicethe height of the beam with a fillet radius extending from the frontface of the seal land to the front face of the beam and the rear and afillet radius extending from the rear face of the seal land to the rearface of the beam;
 7. The invention as claimed in claim 2 wherein therotor blade has a reference normal sectioning plane P passing through apoint at the junction of the transition zone to the airfoil thatcontains a first line perpendicular to the side of the airfoil sectionat that junction point and a second line passing through that junctionpoint that is perpendicular to the first line and parallel to thestacking line of the airfoil; wherein a transition line is the line ofintersection of the plane P with the transition zone at a junction pointand defines the surface contour of the transition zone at a particularlocation; wherein each transition line has an offset distance A from theairfoil which is the distance of the projection of the transition linealong the first line of the plane P perpendicular to the side of theairfoil section, has an offset distance B from the shroud which is thedistance of the projection of the transition line along the second lineof the sectioning plane parallel to the stacking line, and has an offsetratio which is the ratio of the offset distance A from the airfoildivided by the offset distance B from the shroud. wherein eachtransition line has a first end at the junction point and a second endat the point the transition zone terminates, the transition lines beingsmoothly recessed from a straight line connecting the ends of thetransition line.
 8. The invention as claimed in claim 7 wherein thetransition lines extending under the beam are part of a conical section.9. The invention as claimed in claim 8 wherein the transition linesextending under the beam have multiple radii of curvature.
 10. Theinvention as claimed in claim 8, wherein the transition lines extendingunder the beam have a first radius of curvature adjacent the airfoil anda second radius of curvature adjacent the shroud that is larger than thefirst radius of curvature.
 11. The invention as claimed in claim 8wherein the transition lines extending under the beam are part of anelliptical conical section.
 12. The invention as claimed in claim 11wherein the transition lines extending under the beam have multipleradii of curvature.
 13. The invention as claimed in claim 7/1, whereinthe transition lines extending under the beam have a first radius ofcurvature adjacent the airfoil and a second radius of curvature adjacentthe shroud that is larger than the first radius of curvature.
 14. Theinvention as claimed in claim 13/4 wherein the first and second radii ofcurvature each intersect at a point of tangency with the transitionline.
 15. The invention as claimed in claim 13/4, wherein theintersection includes a curved line that is tangent to the first andsecond radii of curvature.
 16. The invention as claimed in claim 14wherein the first and second radii of curvature each intersect eachother at a point of tangency.
 17. The invention as claimed in claim 1wherein the radial thickness of the wings is decreased by the depressionin the wings which decreases airfoil creep as compared to a wing whichdoes not have a radial depression.
 18. The invention as claimed in claim2 wherein the transition zone has a cross-sectional shape which istapered to the side of the wing.
 19. The invention as claimed in claim 7wherein the transition line of the wing, which is also the contour ofthe flow path surface of the shroud for the transition zone of the wing,generally follows the shape of a conical section as the transition lineextends away from the airfoil and the depression above the transitionzone has a spanwise depth at a first lateral location that is smallerthan the spanwise depth of the depression in the wing at a secondlateral location that is laterally closer to the airfoil.
 20. Theinvention as claimed in claim 7 wherein the spanwise depth of thetransition zone at the first location is greater than the spanwise depthat the second location.